{
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   "execution_count": 1,
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multimedia Security Homework 1\n"
     ]
    }
   ],
   "source": [
    "print(\"Multimedia Security Homework 1\")"
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     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
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   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d.axes3d import Axes3D\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams[\"font.sans-serif\"] = [\"SimHei\"] # 用来正常显示中文\n",
    "plt.rcParams['axes.unicode_minus']=False # 用来正常显示负号\n",
    "%config InlineBackend.figure_format = \"svg\"\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "x = np.linspace(-1.5, 1.5, 32)\n",
    "y = np.linspace(-1.5, 1.5, 32)\n",
    "\n",
    "axes3d = Axes3D(fig)\n",
    "X, Y=np.meshgrid(x, y)\n",
    "Z = 255 * (0.36 ** ((X ** 2) + (Y ** 2)))\n",
    "#axes3d.scatter(X, Y, Z, cmap='viridis')\n",
    "axes3d.contour(X, Y, Z, 32, cmap='binary')\n",
    "axes3d.plot_surface(X,Y,Z,alpha=0.5,cmap='gray') \n",
    "axes3d.contour(X,Y,Z,zdir='z', offset=0,cmap=\"gray\")\n",
    "axes3d.view_init(60, 35)\n",
    "axes3d.set_xlabel(\"x\")\n",
    "axes3d.set_ylabel(\"y\")\n",
    "axes3d.set_zlabel(\"强度\")\n",
    "axes3d.set_xticks([-2, 0, 2])\n",
    "axes3d.set_xticklabels([\"$-\\infty$\", \"$0$\", \"$+\\infty$\"])\n",
    "axes3d.set_yticks([-2, 0, 2])\n",
    "axes3d.set_yticklabels([\"$-\\infty$\", \"$0$\", \"$+\\infty$\"])\n",
    "axes3d.set_zticks([0, 127, 255])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '强度')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
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      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axisartist.axislines import SubplotZero\n",
    "%config InlineBackend.figure_format = \"svg\"\n",
    "fig = plt.figure(1)\n",
    "ax = SubplotZero(fig, 111)\n",
    "fig.add_subplot(ax)\n",
    "\n",
    "for direction in [\"xzero\", \"yzero\"]:\n",
    "    ax.axis[direction].set_axisline_style(\"-|>\")\n",
    "    ax.axis[direction].set_visible(True)\n",
    "for direction in [\"left\", \"right\", \"bottom\", \"top\"]:\n",
    "    ax.axis[direction].set_visible(False)\n",
    "\n",
    "plt.grid(b=True, axis=\"y\", linestyle=\"dashed\", linewidth=1)\n",
    "\n",
    "plt.xlim(-2, 2)\n",
    "plt.xticks([-2, 0, 2], \n",
    "           [\"$-\\infty$\", \"$0$\", \"$+\\infty$\"])\n",
    "plt.yticks([127, 255], [\"$127$\", \"$255$\"])\n",
    "ax.axis[\"xzero\"].label.set_text(\"($x_0$,$y_0$)\")\n",
    "z = 255 * (0.3678794 ** ((x ** 2) + (y ** 2)))\n",
    "    \n",
    "ax.plot(x, z)\n",
    "ax.set_title(\"强度\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
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    "import matplotlib.patches as mpt\n",
    "fig,ax = plt.subplots()\n",
    "center = np.array([128, 128])\n",
    "circle = mpt.Circle(center, 2)\n",
    "ax.add_patch(circle)\n",
    "plt.xlim(0, 256)\n",
    "plt.ylim(0, 256)\n",
    "\n",
    "colors = matplotlib.cm.binary_r(np.linspace(0.25, 1, 4))\n",
    "                              \n",
    "for i, c in zip(range(4), colors) :\n",
    "    circle = mpt.Circle(center, 128 - (i * 32), color=c, lw=2)\n",
    "    ax.add_patch(circle)\n",
    "\n",
    "plt.annotate(\"192 - 255\", xy=(128, 128),\n",
    "                           xytext=(-30, 10),\n",
    "                           arrowprops=dict(arrowstyle = \"->\", connectionstyle=\"arc3, rad=.2\"))\n",
    "plt.annotate(\"128 - 191\", xy=(128, 90),\n",
    "                           xytext=(-30, 0),\n",
    "                           arrowprops=dict(arrowstyle = \"->\", connectionstyle=\"arc3, rad=.2\"))\n",
    "plt.annotate(\"64 - 127\", xy=(128, 50),\n",
    "                           xytext=(280, 10),\n",
    "                           arrowprops=dict(arrowstyle = \"->\", connectionstyle=\"arc3, rad=.0\"))\n",
    "plt.annotate(\"0 - 63\", xy=(128, 10),\n",
    "                           xytext=(280, 0),\n",
    "                           arrowprops=dict(arrowstyle = \"->\", connectionstyle=\"arc3, rad=.0\"))\n",
    "    \n",
    "plt.axis('equal')\n",
    "plt.show()"
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  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "# record\n",
    "def corrCC(x, y):\n",
    "    row = x.shape[0]\n",
    "    EX, EY, EXY, EX2, EY2 = np.int(0), np.int(0), np.int(0), np.int(0), np.int(0)\n",
    "    \n",
    "    for i in range(row):\n",
    "        tmpx = x.item(i)\n",
    "        tmpy = y.item(i)\n",
    "        EX += tmpx\n",
    "        EY += tmpy\n",
    "        EXY += tmpx * tmpy\n",
    "        EX2 += tmpx * tmpx\n",
    "        EY2 += tmpy * tmpy\n",
    "\n",
    "    return (row * EXY - EX * EY) / np.sqrt((row * EX2 - EX * EX) * (row * EY2 - EY * EY));\n",
    "\n",
    "# 计算两个矩阵每列之间的相关系数\n",
    "def corrC(x, y):\n",
    "    row = x.shape[1]\n",
    "    col = y.shape[1]\n",
    "    mat = np.zeros((row, col))\n",
    "    for i in range(row):\n",
    "        for j in range(col):\n",
    "            mat[i, j] = corrCC(x[:,i], y[:,j])\n",
    "    return mat\n",
    "\n",
    "corrC(img1, img2) # 用了三重循环，效率很低，但是相关系数矩阵是正确的\n",
    "# 这个函数使用Matlab的corr()函数对应的公式求出，结果是img1的列 × img2的列的矩阵\n",
    "#corrcoef(A, B)"
   ]
  }
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